2 U = -G f faces f 1 .

The Laplacian, defined in eq:laplacian, gives a simple method to determine if the spacecraft has collided with the body [1]}.
The sum \( \sum \omega _f \)  vanishes when outside the body and equals \( -4 \pi \)  inside.
These equations are utilized to compute the gravitational potential of the presented dumbbell spacecraft model.
